The optimum growth rate for population reconsidered

Abstract

Abstract. This article gives exact general conditions for the existence of an interior optimum growth rate for population in the neoclassical two-generations-overlapping model.In an economy where high (low) growth rates of population lead to a growth path which is efficient (inefficient) there always exists an interior optimum growth rate for population.In all other cases there exists no interior optimum. The Serendipity Theorem, however, does in general not hold in an economy with government debt. Moreover, the growth rate for population which leads an economy with debt to a golden rule allocation can never be optimal.

The optimum growth rate for population under critical-level utilitarianism

“…Average utilitarianism cannot be obtained as a special case, but one has to ignore the summation over population (and only compare average utilities). The latter is close to the Samuelson (1975) formulation of optimal population growth, more recently analyzed by Jaeger and Kuhle (2009).…”

Dynamic efficiency and the two-part golden rule with heterogeneous agents

“…In the current case, however, the second term will always be negative for some agents even if r > n. Hence, the results of Galor (1988) and Matsuyama (1991), who show that technological progress may only decrease utility of some agents in an economy which is dynamically inefficient, do not carry over. 15 In a similar fashion, it would now be straightforward to show that the two-part golden rule ceases to serve its watershed role in similar problems, like for example the optimum growth rate for population analyzed in Samuelson (1975a), Michel and Pestieau (1993), and Jaeger and Kuhle (2009), where the first-order condition for optimal population growth for a type l agent dU dn ¼ ÀU c 1 kl À sðlw;rÞ 1þr f 00 ðkÞ dk dn ¼ 0, has the same structure as the foregoing ones. Rather than separating efficient equilibria from inefficient ones, the golden rule separates savers from non-savers as in Propositions 1-3, respectively.…”

“…However, this condition is crucial for the problem of optimal population. Phelps (1968), Samuelson (1975a) and Jaeger and Kuhle (2009) evaluate this condition in detail. It follows from Proposition 1 and Lemma 1 in Jaeger and Kuhle (2009) that the ''yes'' entries in Table 1 of Michel and Pestieau (1993) give the conditions under which such an optimum exists for an economy with CRRA preferences and CES production functions.…”

How powerful is demography? The Serendipity Theorem revisited

“…Taken together, those three conditions characterize usually the optimal levels of c, d, and k for given levels of n and π . Condition 5 defines implicitly the optimum fertility rate: As stressed by Jaeger and Kuhle (2009), it makes explicit the trade-off between the negative capital widening effect (i.e., k) and the positive intergenerational transfer effect i.e., π d n 2 , whose size depends positively on the survival rate π . Those two effects of fertility are playing in opposite directions, so that there seems to be some intuitive support for the existence of an interior optimum fertility rate.…”

“…Thus, Samuelson's result shows the power of demography as an instrument allowing for the decentralization of the long-run social optimum in an otherwise decentralized, perfectly competitive economy. 4 Note, nevertheless, that the scope of Samuelson's results has been somewhat qualified by subsequent studies, such as the ones by Deardorff (1976), Michel and Pestieau (1993), and Jaeger and Kuhle (2009). Whereas those studies cast an important light on the scope of the Serendipity Theorem, these concentrate mainly on the characterization of the economic environment under which Samuelson's result holds, without refining the demographic environment.…”